Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
Abstract
We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included which shows that this is best possible in that: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 1998
- DOI:
- 10.48550/arXiv.math/9811148
- arXiv:
- arXiv:math/9811148
- Bibcode:
- 1998math.....11148C
- Keywords:
-
- Mathematics - Functional Analysis;
- 46B20;
- 46C05
- E-Print:
- to appear: J. of Fourier Anal. and Appl's